Exceptional quantum geometry and particle physics II

Abstract

We continue the study undertaken in [13] of the relevance of the exceptional Jordan algebra $J_3^8$ of hermitian $3\times 3$ octonionic matrices for the description of the internal space of the fundamental fermions of the Standard Model with 3 generations. By using the suggestion of [30] (properly justified here) that the Jordan algebra $J_2^8$ of hermitian $2\times 2$ octonionic matrices is relevant for the description of the internal space of the fundamental fermions of one generation, we show that, based on the same principles and the same framework as in [13], there is a way to describe the internal space of the 3 generations which avoids the introduction of new fundamental fermions and where there is no problem with respect to the electroweak symmetry.

18 pages

References in corpus (2)

• Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra
• $SU(3{)}_C\times SU(2{)}_L\times U(1{)}_Y\left(\times U(1{)}_X\right)$ as a symmetry of division algebraic ladder operators

Cited by in corpus (22)

• Three fermion generations with two unbroken gauge symmetries from the complex sedenions
• The standard model, the Pati-Salam model, and "Jordan geometry"
• Majorana Neutrinos, Exceptional Jordan Algebra, and Mass Ratios for Charged Fermions
• Trace dynamics and division algebras: towards quantum gravity and unification
• Spin(11,3), particles and octonions
• Beyond the standard model with six-dimensional spinors
• Octonion Internal Space Algebra for the Standard Model
• SO(9) characterisation of the Standard Model gauge group
• Why do elementary particles have such strange mass ratios? -- The role of quantum gravity at low energies
• Three generations of colored fermions with $S_3$ family symmetry from Cayley-Dickson sedenions
• The geometry of physical observables
• Quantum gravity effects in the infra-red: a theoretical derivation of the low energy fine structure constant and mass ratios of elementary particles
• Superselection of the weak hypercharge and the algebra of the Standard Model
• The Mass Gap of the Space-time and its Shape
• Causal Fermion Systems and Octonions
• Space-times over normed division algebras, revisited
• Algebraic realisation of three fermion generations with $S_3$ family and unbroken gauge symmetry from $\mathbb{C}\ell (8)$
• Particle models from special Jordan backgrounds and spectral triples
• Jordan Algebraic Interpretation of Maximal Parabolic Subalgebras : Exceptional Lie Algebras
• The Standard Model Symmetry and Qubit Entanglement
• Quantum Spacetime Imprints: The 24-Cell, Standard Model Symmetry and Its Flavor Mixing
• Division Algebras, Triality, and Exceptional Magic